Its just checking rules right? Do it.

Or get a matrix that represents the transformation.

Consider the standard base for .and find the bases for both

Now

So the basis for .

N(T) is .This means Nullity = 0N(T) and R(T). then compute the nullity and rank of T. finally say where it is one -2- one or onto.

R(T) is .

This means R(T) will be the subspace of R3, in which the second co-ordinate is 0.This means Rank = 2.

The map is one-one because nullity is 0.